Startseite Inverse scattering for three-dimensional quasi-linear biharmonic operator
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Inverse scattering for three-dimensional quasi-linear biharmonic operator

  • Markus Harju , Jaakko Kultima ORCID logo EMAIL logo und Valery Serov
Veröffentlicht/Copyright: 6. Januar 2022

Abstract

We consider an inverse scattering problem of recovering the unknown coefficients of a quasi-linearly perturbed biharmonic operator in the three-dimensional case. These unknown complex-valued coefficients are assumed to satisfy some regularity conditions on their nonlinearity, but they can be discontinuous or singular in their space variable. We prove Saito’s formula and uniqueness theorem of recovering some essential information about the unknown coefficients from the knowledge of the high frequency scattering amplitude.

MSC 2010: 35R30; 47A40

Funding source: Academy of Finland

Award Identifier / Grant number: 312123

Funding statement: This work was supported by the Academy of Finland (application number 312123, the Centre of Excellence of Inverse Modelling and Imaging 2018-2025) and by Moscow Centre of Fundamental and Applied Mathematics – MSU, Russia.

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Received: 2020-06-17
Revised: 2021-09-01
Accepted: 2021-11-16
Published Online: 2022-01-06
Published in Print: 2022-06-01

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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